EFFECTS OF PLY CLUSTERING IN LAMINATED COMPOSITE PLATES UNDER - - PDF document

18TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS

1 Introduction This work presents a complete study of the effects of ply clustering on monolithic, flat and rectangular polymer-based laminated composite plates with conventional stacking sequences, subjected to a drop-weight impact loading. Basically, three main tasks are addressed in order to analyze the effects of ply clustering on the damage resistance and on the damage tolerance of the structure, which are: (1) analytical description of the impact test, (2) design and realization of an experimental test plan, and (3) the performance of finite element (FE) virtual tests. Due to the simplicity of the structure, the analytical description of the impact event is feasible. The analytical description presented comprises models which predict the elastic response, and models which predict the threshold load at which significant damage starts. To bridge the analytical elastic prediction of the impact and the onset of damage, the maximum elastic impact force is typically used, and it is compared with a damage threshold

• allowable. Damage occurs if the predicted elastic

impact force is greater than an appropriate threshold for the corresponding dynamic response type. The analytical description is suitable for preliminary design analysis, as it enables the fast assessment of the role that each parameter plays in the impact

• event. In this sense, the analytical description is used

mainly for the definition of the experimental test plan. On the other hand, the experimental test plan covers: non-destructive inspections (NDI) for the detection

• f manufacturing flaws, drop-weight impact tests,

NDI inspections after impact to assess the damage resistance, and finally, compression after impact (CAI) tests to assess the damage tolerance of the structure. Finally, FE simulations of the drop-weight impact and the CAI tests are performed by using well-suited constitutive models formulated in the framework of Continuum Damage Mechanics. In detail, an interlaminar constitutive model to describe the delamination, and an intralaminar constitutive model to describe the matrix cracking and the fiber breakage damage mechanisms, are used. The purpose of these simulations is double: on the one hand, to validate the suitability of the numerical simulations by comparing with the experimental data, and on the other hand, to provide more clarifying information to analyze the experimental results. 2 Analytical Prediction And Tests Definitions To determine the maximum elastic impact load, the impact characterization diagram proposed by Yigit and Christoforou is used [1]. Given an impact configuration, the diagram predicts the behavior type and the maximum impact force by calculating only two key dimensionless parameters: λ (relative stiffness) and ζw (relative mobility [2]). They are respectively defined as:

bs

k k =

α

λ (1)

1

1 16

i w *

k M I D =

α

ζ (2) where kbs is the bending-shearing plate stiffness, kα is the stiffness of the contact law which relates the impact load with the indentation of the impactor on the plate, Mi is the impactor mass, I1 is the plate mass divided by the in-plane area. The term D* is

EFFECTS OF PLY CLUSTERING IN LAMINATED COMPOSITE PLATES UNDER LOW-VELOCITY IMPACT LOADING

E.V. González1*, P. Maimí1, P.P. Camanho2, A. Turon1, J. Costa3

1 Department of Engineering Mechanics, University of Girona, Girona, Spain, 2 Department of Engineering Mechanics, University of Porto, Porto, Portugal, 3 Department of Physics, University of Girona, Girona, Spain,

* Corresponding author (emilio.gonzalez@udg.edu)

Keywords: ply clustering, polymer-based laminated composite, low-velocity impact, CAI, finite element

called effective plate stiffness (for more details, see [1]). The diagram is shown in Fig. 1 and represents the variation of the maximum normalized impact force

max

F as a function of the relative mobility parameter ζw. Four different regions can be identified in the diagram those define four different impact

• behaviors. Impact configurations which define

points in the right part of the diagram behave as quasi-static. For points which fall close to the dashed curve behave as in-plane infinite plate. Between the quasi-static and the infinite plate behaviors there is a transition zone where the resulting response is a combination of both behaviors. Finally, the points that fall close to the maximum dimensionless force result in the half-space behavior, i.e. the plate response is neglected. Fig.1. Impact characterization diagram (after [1]). In order to demonstrate the validity of the characterization diagram, several impact situations covering all behavior type regions were predicted by Yigit and Christoforou [1], by numerical integration

• f a complete analytical model which considers

classical laminated plate theory, simply supported boundary conditions and a linear contact law. As shown in Fig. 1, the simulations follow reasonably well the trends of the characterization diagram, although in the transition zone, a complete analytical model is required in order to better describe the response. The analytical criterion used for the onset of the delamination was proposed by Davies and Robinson [3]. The model is based on Linear Elastic Fracture Mechanics (LEFM) and assumes that mode II fracture determines delamination growth in a simply supported circular plate. To simplify the development of the model, static loading conditions were considered, the laminate was treated as isotropic, and

• nly

small deflections were

• considered. Knowing that GIIc is the fracture

toughness in pure mode II, the criterion is defined as: 32 3

* IIc d

D G F = π (3) The ASTM D7136/D7136M-05 [4] test method for measuring the damage resistance of a fiber- reinforced polymer matrix composite when subjected to a drop-weight impact event is taken as a reference in order to fix some of the governing

• parameters. The standard is focused on rectangular,

flat and monolithic laminated composite plates with 150 mm x 100 mm in-plane dimensions. The specimens are placed over a flat support fixture base with a 125 mm x 75 mm rectangular cut-out which allows the impactor to contact through the specimen without interferences. The support fixture base has four rubber-tipped clamps which restrain the specimen during impact. The boundary conditions provided by the edge supports can be approximated to simply supported. The stacking sequences proposed here to study the ply clustering effect are [(45/0/-45/90)4]S, [(452/02/- 452/902)2]S, and [454/04/-454/904]S (in the following, these laminates are respectively identified as L1, L2, and L4). The plate stacking sequence is defined by taking the 0º fiber orientation aligned with the longer in-plane dimension of the plate. All laminates have the same plate thickness h because an equal number

• f plies is used (i.e. 32 plies; h = 5.8 mm). However,

the ply thicknesses hp are different (i.e. L1: hp = hpp, L2: hp = 2hpp, and L4: hp = 4hpp, where hpp is the thickness of a single pre-preg ply), yielding to different number of interfaces for delamination (i.e. L1: n = 30, L2: n = 14, and L4: n = 6). The plates were manufactured using Hexply AS4/8552 carbon- epoxy unidirectional pre-preg. Three different impact energies Ei are considered: 19.3 J, 28.6 J, and 38.6 J. Given that the impactor mass is kept constant at 5 kg, the different energies also enable the study of the effects of velocity. Since the repeatability of the impact test is quite good, a

EFFECTS OF PLY CLUSTERING IN LAMINATED COMPOSITE PLATES UNDER LOW-VELOCITY IMPACT LOADING 3

sample of less than three specimens is used for some cases: Lx-S1 and Lx-S2 for 19.3 J, Lx-S3 for 28.6 J, and Lx-S4 to Lx-S6 for 38.6 J (where x: 1, 2 and 4). Using the corresponding material properties, the impact characterization parameters resulted: λ = 1.62 and ζw = 4.48 for L1, λ = 1.60 and ζw = 4.50 for L2, and λ = 1.55 and ζw = 4.58 for L4. Since the key parameters are independent of the impact velocity, the resulting values are constant for each laminate at any impact energy. Additionally, the key parameters are almost equal for all laminates due to the fact that the stiffness of the laminates is similar. Therefore, the dimensional elastic response of the laminates for each impact energy is also expected to be similar. Introducing the key parameters in the impact characterization diagram, a quasi-static behavior and a maximum dimensionless force of

max

F

= 0.78 are

predicted for all the laminates (see Fig. 1). Using the dimensionless framework, the maximum dimensional elastic forces for each impact energy are: Fmax = 14.0 kN for Ei = 19.3 J, Fmax = 17.1 kN for Ei = 28.6 J, and Fmax = 19.8 kN for Ei = 38.6 J. On the other hand, the values of the delamination threshold (Equation (3)) are: 8.53 kN for L1, 8.49 kN for L2 and 8.34 kN for L4. These thresholds are constant for each impact energy since no dependence with velocity is considered in the

• formulation. As expected, the values obtained are

practically the same for all laminates. In addition, the delamination occurrence is assured for all impact energies since the values of the peak load are greater than the delamination thresholds. 3 Experimental Results

• Figs. 2 and 3 show the histories of the impactor

reaction force for each impact energy of laminates L1 and L4, respectively. An interesting observation is that the experimental threshold load, Fd, at which significant loss of stiffness occurs, remains constant for each laminate independently of the impact

• energy. Therefore, Fd is independent of the impact

velocity since the impactor mass is the same for all the energies defined. In addition, the determination

• f the threshold load for laminate L1 can be easily

identified whereas for the laminate with the thickest plies, L4, this identification is more difficult. Moreover, the whole profiles of the force histories of laminate L4 do not have the large oscillations which

• ccur for laminate L1. This fact indicates that

changes in the stiffness during the impact are expected to be more progressive and smooth for laminates with thick plies than for laminates with thin plies. This behavior can be caused by the large matrix cracks which can occur when the plies are thick. Fig.2. Impact force histories of laminate L1. Fig.3. Impact force histories of laminate L4. Despite the fact that all the laminate types considered have practically the same stiffness, the resulting impact force histories are clearly different from the point where significant damage starts. This is due to the differences in the ply thicknesses of the laminates, and further highlighted in Figs. 4 and 5, which compare the results for the different laminates for each impact energy 19.3 J, 28.6 J and 38.6 J. The first part of the results is the elastic regime of the impact process which is common for all laminates at each impact energy. However, the points where significant damage starts are clearly different, and from these points, the force histories separate and follow different paths. It can be observed that the predictions of Fd given by equation (3) are far from the experimental values, especially for laminate L4. This result is due to the fact that the effect of the ply thickness is not accounted in the development of the load threshold,

in addition, the assumption that a single delamination can generate a drop in the impact force history is not fully clear. Furthermore, Figs. 4 and 5 show that the impact response is elongated by increasing the ply clustering of the laminate. Since delaminations cause a reduction of the stiffness, it is clear that larger delaminations should develop for laminate L4 because less interfaces are available for delamination in comparison with the

• ther

laminates. Fig.4. Impact force histories for 19.3 J. Fig.5. Impact force histories for 38.6 J.

• Fig. 6 shows a sample of the C-scan inspections of

each laminate type for each impact energy. It is

• bserved that by increasing the impact velocity the

projected area increases for all the laminates. In addition, by reducing the number of interfaces available for delamination, the resulting projected delamination area is increased. This result is also related to the impact force histories (see Figs. 4 and 5), where the responses for laminate type L4 are larger since the bending stiffnesses are reduced due to the large delaminations created. Finally, the mean residual compressive loads

• btained in the CAI tests [5] for each laminate type

are: FL1 = 133 kN, FL2 = 134 kN and FL4 = 105 kN for 19.3 J; FL1 = 103 kN, FL2 = 100 kN and FL4 = 103 kN for 28.6 J; and FL1 = 96 kN, FL2 = 90 kN and FL4 = 98 kN for 38.6 J. It is observed that increasing the impact energy (or the impact velocity), the residual compressive loads are reduced for all the laminates

• tested. In addition, the damage tolerance estimated

by means of the residual compressive load does not seem to be reduced by increasing the ply thickness, because all laminate types show similar values of the residual compressive load at each impact energy. This result is due to the fact that the compressive load depends on a combination of variables such as the number of delamination planes, the size of the delaminations, and their locations through-the- thickness of the laminate. Fig.6. Sample of C-scan inspections of laminates L1, L2 and L4. 4 Numerical Simulations And Comparison With Experimental Results For the FE simulations, each laminate is modeled such as each ply clustering is modeled by a single layer of 3D solid elements, at which an intralaminar damage model is assigned. In addition, cohesive elements described by means of a delamination model are introduced only between plies with different fiber orientation. All plies are modeled using solid elements. Therefore, the FE models require the formulation and the implementation of two constitutive models: interlaminar model to describe the delaminación (González et al. [6]) and an interlaminar model to describe the matrix cracking and fiber breakage (Maimí et al. [7-8]). The FE code used is Abaqus/Explicit [9]. The models have been parallelized in 24 CPUs, with 2GHz each

• ne. The whole runtime analysis of the impact and

EFFECTS OF PLY CLUSTERING IN LAMINATED COMPOSITE PLATES UNDER LOW-VELOCITY IMPACT LOADING 5

CAI tests has ranged between twelve and fifteen days, depending on the plate stacking sequence.

• Figs. 7 and 8 show the comparisons between the

experimental and the numerical evolutions of the impact force of the laminate L4 for 19.3J and 38.6J. As can be observed, the whole profiles and the contact times are quite well predicted, whereas the damage thresholds Fd are clearly over-predicted. Moreover, in contrast with the experimental results, it is detected that the numerical values of Fd are not kept constant by changing the impact velocity. Fig.7. Experimental and numerical impact force histories of the laminate L4 for 19.3 J. Fig.8. Experimental and numerical impact force histories of the laminate L4 for 38. 6J. As an illustrative example, Fig. 9 shows the experimental and the numerical evolution of the absorbed energy, Ea, of the laminate L4 for 19.3J. As can be observed, the numerical prediction fits well the experimental profile. The FE simulations have been modeled so the whole energy of the system can be split into the different energy components, allowing to know the role that plays each one at any moment of the impact event. Accordingly, the evolutions of the energy dissipated due to delamination, EDd, and the intralaminar damage mechanisms (EDm: matrix; EDf : fiber), are plotted separately in Fig. 9. It can be observed that the main dissipative mechanism is the delamination. Fig.9. Experimental and numerical evolutions of the absorbed energy.

• Fig. 10 shows the predicted delamination area at two

different contact times: ti = 0.4 ms (just before to reach Fd), and ti = 0.8 ms (just after the first drop of the impact force). The field variable plotted corresponds to the scalar damage variable of all the interface elements, so a translucency is applied in

• rder to visualize all the interfaces. These

projections are such as the images that can be

• btained by C-scan inspections. It can be observed a

large and quick increase of the delaminations between these two instants of time. Fig.10. Projected delaminated area for impact times: ti = 0.4 ms and ti = 0.8 ms. According to the numerical predictions, a certain number of delaminations propagate simultaneously at the critical point Fd. Therefore, the development

• f analytical damage thresholds based on the

assumption that a single delamination can generate a drop in the impact force history, is not fully clear.

ti = 0.4 ms ti = 0.8 ms

Acknowledgements This work has been partially funded by the Spanish Government (Ministerio de Ciencia e Innovación) under Contracts MAT2009-07918 and DPI2009- 08048. References

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